Improvement in scale-rules



W. HAY.

Y Scale Measure.

No. 65,744. I Patented June 11, 1867.

N.PEIERS. PHOTO-UYHQGRAPMER, WASHINGTON. D. C

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WILLIAM HAY, OF DUMBARTONi SCOTLAND, A-S SIGNORTO ROBERT HAY, OF MINERALPOINT, WlSOONSlN.

Letters Patent No. 65,744, dated June 11, 1867.

IMPROVEMENT 11v SCALE-RULES.

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TO ALL WHOM IT MAY CONCERN:

Be it known that I, WILLIAM HAY, of Duinbarto'n, in the county ofDumbarton, in that part of the United Kingdom of Great Britain andIreland known as Scotland, have invented a new and improved Scale-Rule;and I do hereby declare that the following is a full, clear, and exactdescription of the same, reference being had to the accompanyingdrawings, making a part of this specification, in which- Figure 1represents that side of the rulewhich I denominate the side of equalsquares, the rule being in a closed or folded condition.

Figure 2 represents the opposite side of the rule, the rule beingextended or opened out.

Figure 3 shows the side of equal squares, and the position of the rulewhen used for dividing a circle into equal parts or segments.

Similar letters of reference indicate corresponding parts in all thefigures. r

This invention consists in the construction of a rule for the use ofmechanics, with scales, whereby the rule may be cmployednot only formeasuring surfaces in the ordinary way, but also for ascertaining thecircumference of a circle of any given radius; also, for finding theside of a square equal to the area of a given circle; also, for findingthe radius of a circle equal in area to a given square; also, fordividing a circle into any desired number of equal parts; and,furthermore, for finding the side of the greatest square that can beinscribed within a given circle; and also the circle that willcircumscribe a given square, thus rendering the rule capable of muchmore universal employment in difierent kinds of work than thoseheretofore in use.

To enableothers to understand the nature and construction of myinvention, I will proceed to describe it,

with reference to the drawings.

The several figures represent a jointed two-foot rule, on the outer edgeof each side of which is a scale, an, marked in inches, and subdividedby eighths of an inch, in the same manner as a rule of ordinaryconstruction. Marked upon that side of the rule shown-in fig. 2, and atthe inner edge thereof, or, in other words, at the edge opposite thescale a a of the said side, is another scale, 6 6. Of the divisions ofthis scale 15 b there are 3.14159 to the inch, so that the number ofdivisions in the scale I) b are in the same proportion to the number ofthose of the scale a a as the circumference of a circle is to thediameter thereof, in order that the diameter of a circle being measuredby the scale a a, the circumference thereof will be indicated by thescale 6 b at a point exactly opposite that point on the scale a a whichindicates the diameter of the circle; thus, for instance, if thediameter is shown at a on the scale a a, the circumference will be shownat b on the scale I; b. The divisions of the scale 6 b are numberedconsecutively from one upward, and are subdivided each into eight, orany other desired or suitahle'numher of equal parts, as shown in theaforesaid fig; 2. The opposite side or surface of the rule isrepresented in figs. 1 and 3, and on one'leg of the rule. Upon the saidside thereof is another scale, a e, which is situated just within thescale a a of the said side, on what I denominate the line of chords.

The chord-scale C1. is divided into ninety parts or degrees, which areso graduated as to diminish in length from one upward, in the sameproportion that the sides of a square diminish'when inscribed withincircles having a less radius and which are indicated by figures ornumbers, placed at suitable intervals along the said scale. As shown inthe drawings, the length of this scale a a is equal to the side of thelargest square that can be inscribed within a circle having a radiusof'six inches. Formed upon thesame side of the rule, one upon each ofthe legs'thereof, are two radius-scales d d, which are identical inconstruction. Each scale d d extends from the centre a of the joint or.hinge of the rule to the outer end of the arm on which it is formed, andis situated at a slight angle to thcedge thereof, in such manner thatwhen the rule is folded or closed, as shown in the said fig. 1, the saidscales will be placed at an angle or inclination with reference to eachother, both radiating from the common centre 0'. These radius-scales areeach divided into twelve equal parts, which are indicated by suitablenumerals, the said divisions being further subdivided into eighths, inthe same manner as the scale a a. Inasmuch as thc radius-scales d 61extend the ,whole length ofthc logs of the rule upon which they areformed, the centre of each of the said scales is at the point indicatedby the fig. 6, the division lines in one scale being exactly oppositethose on the other.

